physical models for nic eos, opacity, transport, … · physical models for nic eos, opacity,...
TRANSCRIPT
LLNL-PRES-557971
Physical Models for NIC EOS, Opacity, Transport, Nuclear, Kinetics
J. Wark and G. Collins
P. Sterne, C. Mauche, S. Hamel, B. Heeter, R. Rygg, E. Schwegler, D. Clark, S. Haan, L. Benedict, J. Gaffney, D. Fratanduono, P. Celliers, Y. Ping, O. Landen, J. Eggert, R. Marrs, C. Bellei, P. Amendt, S. Wilks, M.
Akin, J. Hammer, C. Iglesias, D. Hicks, H. Scott, J. Castor, A. Lazicki, B. Wilson, T. Luu, D. McNabb, G. Zimmerman
LLNL-PRES-557971
Several physical models are important for manipulating HED matter to ignition
2 LLNL-PRES 557971 dT/dx
Fuel assembly, transport,burn-physics
PLS
Laser Energy = 1.3 MJ
X-ray Energy = 1 MJ
Energy to capsule =120 kJ Set adiabat
Fuel K.E. = 12 KJ, Shell K.E. ~ 20 KJ
Hot spot = 10KJ
Burn propagation
LLNL-PRES-557971
3
Laser Energy = 1.3 MJ
X-ray Energy = 1 MJ
Energy to capsule =120 kJ Set adiabat
Fuel K.E. = 12 KJ, Shell K.E. ~ 20 KJ
Hot spot = 10KJ
Burn propagation
Opacity, laser-plasma interaction, heat & e-transport
Ablator opacity & EOS, drive Spectrum,radiation,e- production & transport
Ablator opacity, drive spectrum, heat & radiation transport, CH & DT EOS
Heat transport, MIX, CH & DT EOS, Kinetics
Transport, MIX, CH& DT EOS, Bremmstrahlung, reaction rates, Kinetics
dT/dx
Fuel assembly, transport,burn-physics
Several physical models are important for manipulating HED matter to ignition
LLNL-PRES 557971
LLNL-PRES-557971
Several NIC discoveries are motivating improvements in our physical models
• Drive and ablation physics:
• Implosion velocity, Vimp, is low (EOS, Opacity, drive, Kinetics)
• Vimp difference between Si and Ge capsules (Opacity, drive)
• Ablator is thicker than predicted (EOS, NLTE, e- transport)
• Ablator release into D2 shows was initially off (EOS)
• Matching shock timing data with simulations requires drive multipliers (EOS, Opacity, drive, LPI)
• Stagnation Physics and Mix:
• Yield for a given Vimp and rho-R is low (EOS, Kinetics, transport)
• Hot spot pressure is low (EOS, Kinetics, transport)
• More low energy neutrons (<9MeV) than expected (Nuclear, kinetics)
• τNuclear Burnwidth > τx-ray burnwidth (transport)
• Mix cliff occurs at higher ablator mass than expected (Transport, kinetics) LLNL-PRES 557971
LLNL-PRES-557971
Our panel will break up into groups focused on physical models, in contrast to implosion stages
Drive Tr(t), drive spectrum
Implosion dynamics
Bangtime, Vimp, shell thickness, shk timing
Stagnation Physics Yield, PHS, rho-R, Ti
Mix Atwood #
Opacity
EOS
Transport
Kinetics
Nuclear
Au, U
Implosion Performance and NIC Observables Physical models
LLNL-PRES 557971
LLNL-PRES-557971
• Ablator opacity (C, Si, Ge) is important for tuning ablation performance, mix and preheat.
• Both NLTE and LTE opacities have been improved recently (H. Scott, S. Hansen, HEDP 6, (2010). B.G. Wilson, et al PRE 76, 032103 (2007). ) but still DCA differs from more sophisticated models and EOS and Opacity are not self consistent.
• Important to consider convergence effects in photon binning and material zoning while considering effects of Opacity (Hill and Rose).
Optimizing implosion performance requires accurate opacities and emissivities (Si, C, Ge, Au, U)
C, Ge and Si opacity at .1g/cc and 300 eV
Energy (eV) κ
(cm
2 /mol
e)
Bν
kT=300 eV ρ=0.1 g/cc
C Si
Ge
106
102
10-2
100 1000 10,000
300 eV black body
Preheat shielding
Preheat X-rays (>~1.8 keV)
LLNL-PRES 557971
LLNL-PRES-557971
ICF requires knowledge of the hohlraum, ablator and fuel EOS over a broad range of conditions
Cold curve
GDP ablator
Dashed Hugoniot
Pres
sure
(Mba
r)
Density (g/cc)
Complex chemistry
Trajectory for glow discharge polymer (GDP), CH1.3 ablator in ICF implosion
Ablation
Ionization e- thermal
100
10
1
0.1
0.01 10 20 2 1 5
We need to know DT to 1.5 Kg/cc
Other ablator candidates include diamond, Be, B4C, Al LLNL-PRES 557971
LLNL-PRES-557971
Transport processes implicit to forming a burning plasma are largely untested in relevant regeims
• e-ion coupling in hot spot & dense fuel: • Stopping power in hot spot & dense fuel: • Thermal conductivities hot spot & dense fuel: • Thermal conductivities in CH
Slightly more detailed example (Steve Rose)
• Viscosity models…..
• How to handle mixtures…..
• Bremmstrahlung
• Compton scattering
α
n
radiation Inelastic collisions
Inelastic collisions
Inelastic collsns em+nuclear
nuclear reactions
bremmsstrahlung/ scattering
thermal non-thermal
free electrons
Inelastic collisions
Inelastic collisions DT ions
For Te < 32keV
Thermal conductivity is important for predicting mix and hotspot dynamics
Purgatorio and QMD are in good agreement with D2 data on-Hugoniot but not off-Hugoniot
D2 Data compared to Purgatorio Hugoniot
Off-Hugoniot
Variations in thermal conductivity of a few times effect hydrodynamics at 10g/cc and 10eV
Experimental data: Nellis1992, Nellis1999, Celliers2000, Fortov2003, Ternovoi2009, This work Shell radius (µm)
Theory: Purgatorio from Sterne et al.
LLNL-PRES 557971
LLNL-PRES-557971
11
Thermonuclear (TN) burn in DT plasma involves many complex processesof comparable time scales that compete with dis-assembly
fi(e)
E (keV)
TT= 76 keV
TD= 93 keV
0.01
0.1
1
10 100T (keV)
!"-e /!fusion
!"-DT /!fusion
E" ~ 1 MeV
"'s couple first to electrons,then to ions as T increases
D & T distributions differ& Not quite Maxwellian
" stopping moderates TN burn
Tem
pera
ture
(keV
)
Time (ns)
D
T
electron
radiation
#T$
!" = 0!"
Use VPIC code to simulate infiniteD-T plasma @ % = 100 g/cc, T = 10 keV
Bowers et al., Phys Plasma 15, 55703 (08)
Kinetic ions, D, T, "'s
Fluid electrons
Radiation energy sink
Need to coupleresults to ICFdesign code
Brian Albright
Thermonuclear burn in DT involves many complex processes of comparible time scales that compete with confinement time
G. Dimonte et al
Dimonte
11
Thermonuclear (TN) burn in DT plasma involves many complex processesof comparable time scales that compete with dis-assembly
fi(e)
E (keV)
TT= 76 keV
TD= 93 keV
0.01
0.1
1
10 100T (keV)
!"-e /!fusion
!"-DT /!fusion
E" ~ 1 MeV
"'s couple first to electrons,then to ions as T increases
D & T distributions differ& Not quite Maxwellian
" stopping moderates TN burn
Tem
pera
ture
(keV
)
Time (ns)
D
T
electron
radiation
#T$
!" = 0!"
Use VPIC code to simulate infiniteD-T plasma @ % = 100 g/cc, T = 10 keV
Bowers et al., Phys Plasma 15, 55703 (08)
Kinetic ions, D, T, "'s
Fluid electrons
Radiation energy sink
Need to coupleresults to ICFdesign code
Brian Albright
11
Thermonuclear (TN) burn in DT plasma involves many complex processesof comparable time scales that compete with dis-assembly
fi(e)
E (keV)
TT= 76 keV
TD= 93 keV
0.01
0.1
1
10 100T (keV)
!"-e /!fusion
!"-DT /!fusion
E" ~ 1 MeV
"'s couple first to electrons,then to ions as T increases
D & T distributions differ& Not quite Maxwellian
" stopping moderates TN burn
Tem
pera
ture
(keV
)
Time (ns)
D
T
electron
radiation
#T$
!" = 0!"
Use VPIC code to simulate infiniteD-T plasma @ % = 100 g/cc, T = 10 keV
Bowers et al., Phys Plasma 15, 55703 (08)
Kinetic ions, D, T, "'s
Fluid electrons
Radiation energy sink
Need to coupleresults to ICFdesign code
Brian Albright
LLNL-PRES 557971
LLNL-PRES-557971
Electron ion equilibration is important for hotspot dynamics, shock equilibration, and laser coupling
5
Thermonuclear burn in ICF plasma involves many collisionaltransport processes whose rates can be improved
D
T !
n D
e
T
3.5 MeV
14.1 MeV"i-e
Radiation
0.01 0.1 1 10
T (keV)
1
10
102
103
104
Bremsstrahlung
Fusionion-electron#T ~ 0.1 T
$ = 100 g/cc
dEdt
Thermonuclear processes in ICF
Transport rates depend on long-rangeCoulomb collisions
Maxwellian electrons & ions
Thermal relaxation
Thermal conductivity
Electrical conductivity
Radiative
dTi
dt~ ! ie Te " Ti( )
! process ~ !o ln# process $n
Te3/2ln
bmax
bmin
%
&'(
)*
Temperature decay not exponentialbecause " % T-3/2
Uncertainty in Coulomb log
(relativistic correction)(degeneracy correction)
6
Legacy calculations of temperature relaxation between electrons& ions diverge due to Coulomb force ! r-2
!o
=8
3
2"m
M
e2ei
2
T3 / 2
n
i
e
b
Particle collisions can be described by integrating Rutherford cross-sectionin Boltzman equation, but this diverges due to distant encounters
a !3
4"n#
$ %
&
' (
1/ 3
!ie
= !o
b db
b2
+ Ze2/mv
2( )2
0
bmax
"
!ie
=!o
2ln 1+ 3
bmax
bmin
#
$ %
&
' (
2#
$
% %
&
'
( (
bmin
=Ze
2
kBTe
bmax
)*
Screening parameter bmax
!De
=kBT
4"ne2
!DH
=!De
1+ Z
a =4"n3
#
$ %
&
' (
)1/ 3
Spitzer:
Landau:
Chandrasekhar:
"Dei
Plasma fluctuations (#(k,$) ~ 0) due to discrete electrons & ions aredescribed by Lenard-Balescu, but this diverges due to close encounters
!ie
= !o
k3dk
k •" k,0( ) • k2
0
kmax
#
!ie
= !o
dk
k
k4
k2
+ kDe
2( )2
0
kmax
# = !oln
$De
bmin
%
& '
(
) *
kmax~1
bmin
+,
Need to capture close & distant encounters self-consistently
bmin ~ 1 / kmax
RL =Ze
2
kBT
!Q =!
mkBT
Landau:
deBroglie:
Particle collisions can be described by integrating Rutherford cross-section in Boltzman equation, but this diverges due to distant encounters Plasma fluctuations due to discrete electrons & ions are described by Lenard-Balescu, but this diverges due to close encounters
LLNL-PRES 557971
LLNL-PRES-557971
Electron ion equilibration is important for hotspot dynamics, shock equilibration, and laser coupling
Log(Λ) for hydrogen Lee and More (solid), GMS (dotted), BPS(dashed)
20 40 60 80 100density �g�cc�
5�10�13
1�10�12
2�10�12
5�10�12
1�10�11Tau electron�ion at 1 KeV
Electron ion equilibration time for Lee and More (red), GMS(blue), and BPS (green)
Equilibration times are ~ps while burn durations 10-100 ps
LLNL-PRES 557971
LLNL-PRES-557971
Stopping of charged particles is dominated by electron-ion interactions and contains ion-ion scattering
Alpha stopping
dEdx
=CiondEdx i
+CiondEdx e
+CiondEdx b
Contribution from Ions Free e- Bound e-
Details for stopping power
Te=1 KeV, ne= 5e25
dE/d
x (M
eV/m
icro
n)
.8
.4
0 0 2 4
Vp/Ve Vp/Ve
Te=10 KeV, ne= 1e24
dE/d
x (M
eV/m
icro
n)
0 2 4
.004
.002
0
NIC estimate: solid BPS: Circles Landau & Lifshitz: dashed Li & Petrasso: triangle
LLNL-PRES 557971
LLNL-PRES-557971 Summary of candidate multi-species and kinetic effects Shock Separation
Frictional Shock Heating of DT Heating Due to Tail of Distribution
Species Separation in Ablator
Pressure gradient-induced E-field causes lighter species to accelerate ahead of heavier species
Some fraction of ablation energy goes into separating C from H, resulting in loss of ablation efficiency
During hot spot formation, electrons in tail of energy distribution (~10 X Te) may heat fuel
Ion coupling heats T in front of T shock
D shock hits r=0 first T
[keV
]
Radius [µm] 0 100 200
1
2
3
4
--- Kinetic --- Fluid
T shock lags
Shocks in dense plasma cause relative drift speed between species: energy in directed V goes into heat
!M =Ni
2!H +!C + 7!e " kBT 2 ln9+ 7ln 9 / 7( )( )#$ %& !U =!M +"!
CH C H 1-c1 c1
Fuel region
T ion
[eV
]
40
60
80
100
120 130 140
Hot Spot
Radius [µm]
E-field Pressure
D D
D D
D D
D D
D D D D D
T D
D D
D D D
Shock front structure
Ther
mal
sho
ck p
recu
rsor
T T T
T
T T
T T T
T T
T
T T T
T T
T
e- e-
e-
e-
e- e-
e-
e-
e-
e-
e-
e- e-
e-
e- !!d !
2!i!" 2DkE #
e!E
kBT
@ 2.5 ps
LLNL-PRES 557971
LLNL-PRES-557971
Thermonuclear Burn as well as nuclear diagnostic data interpretation depend on nuclear reaction rates
D-T reaction rate is extremely dependent on Tion. α-particles can heat up electrons and ions differently.
LLNL-PRES-557971
The first nuclear cross section measurement using an ICF facility has been made at Omega
Measurements of the Differential Cross Sections for the Elastic n-3H and n-2H Scatteringat 14.1 MeV by Using an Inertial Confinement Fusion Facility
J. A. Frenje, C. K. Li, F. H. Seguin, D. T. Casey, and R.D. PetrassoPlasma Science and Fusion Center, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
D. P. McNabb, P. Navratil, and S. QuaglioniLawrence Livermore National Laboratory, Livermore, California 94550, USA
T. C. Sangster, V. Yu Glebov, and D.D. Meyerhofer*
Laboratory for Laser Energetics, University of Rochester, Rochester, New York 14623, USA(Received 18 June 2011; published 15 September 2011)
For the first time the differential cross section for the elastic neutron-triton (n-3H) and neutron-deuteron(n-2H) scattering at 14.1 MeV has been measured by using an inertial confinement fusion facility. In these
experiments, which were carried out by simultaneously measuring elastically scattered 3H and 2H ions
from a deuterium-tritium gas-filled inertial confinement fusion capsule implosion, the differential cross
section for the elastic n-3H scattering was obtained with significantly higher accuracy than achieved in
previous accelerator experiments. The results compare well with calculations that combine the resonating-
group method with an ab initio no-core shell model, which demonstrate that recent advances in ab initio
theory can provide an accurate description of light-ion reactions.
DOI: 10.1103/PhysRevLett.107.122502 PACS numbers: 25.40.Dn, 52.57.!z
The development of an accurate description of light-ionreactions is currently of great interest as it would providevaluable insight into low-energy nuclear reactions impor-tant to nuclear astrophysics. Radiative capture reactions, forexample, occur in red giants at temperatures low enoughthat the reaction rates are too small to be directly measuredin a laboratory. Extrapolation from measurements at higherenergies is also suspect without a fundamental theory forcomputing these reactions. Fusion energy research alsorequires accurate cross sections for light-ion reactions toconstrain models of inertial confinement fusion (ICF) ex-periments involving deuterium-tritium fuel. For instance,uncertainties in the differential cross section for the elasticn-3H scattering need to be"5% to reliably infer a fuel arealdensity (!R) from the yield ratio between scatteredneutrons and primary 14.1-MeV neutrons, called thedown-scatter ratio [1], produced in an ICF implosion. Thedetermination of the!R from the down-scatter ratio value isessential for understanding how the fuel is assembled in animplosion and for ultimately guiding the community to-wards the demonstration of thermonuclear ignition and netenergy gain [2] at the National Ignition Facility [3].
Since the 1950s, the differential cross section for theelastic n-3H scattering at 14.1 MeV has been subject toboth experimental and theoretical studies. Kootsey [4]measured the cross section at center-of-mass (CM) anglesranging from 55# to 165#, resulting in data with statisticaluncertainties of "20% and a systematic uncertainty of11%. Shirato et al. [5] and Debertin et al. [6] measuredthe cross section in the CM angular range of 100#–175#
with an uncertainty varying from "10% to "70%, and
their results are in good agreement with each other but upto a factor of 2 smaller than the Kootsey data. Optical-model calculations conducted by DeVries et al. [7] and bySherif and Podmore [8] reproduced the Shirato andDebertin data in this CM angular range. Additionally,Hale et al. [9] conducted an R-matrix analysis of allexperimental data sets, and the result from that analysisforms the basis of the current ENDF/B-VII evaluation [10]of the differential cross section for the elastic n-3H scat-tering that can be found in nuclear databases. Althoughefforts have been made to quantify this fundamental crosssection, significant discrepancies exist between the differ-ent measurements and between measurements and models.However, a theoretical understanding of the n$ 3H scat-tering based on first principles calculations is within reach[11]. For example, ab initio variational calculations using ahyper-spherical harmonics basis expansion performed witha modern nuclear Hamiltonian consisting of an accuratenucleon-nucleon potential and a three-nucleon interactionprovide a good description of the differential cross sectionfor elastic n$ 3H scattering at low energies [12]. However,this type of calculation is currently limited to energiesbelow the breakup threshold.This Letter describes the first measurement of the dif-
ferential cross section for the elastic n-3H scattering at14.1 MeV by using an ICF facility. It also describes atheoretical calculation [13] of this cross section, whichcombines the ab initio no-core shell model [14] with theresonating-group method [15] into a unified method(NCSM/RGM) [16]. By using this theoretical approach,an accurate assessment of the n-3H cross section can be
PRL 107, 122502 (2011) P HY S I CA L R EV I EW LE T T E R Sweek ending
16 SEPTEMBER 2011
0031-9007=11=107(12)=122502(5) 122502-1 ! 2011 American Physical Society
Simultaneous measurements of d’ and t’ spectra scattered by d-t neutrons.
Comparison with ab initio calculations
1. P. Navrátil et al., LLNL-TR-423504 (2010). 2. Ga.A. Hale et al., Phys. Rev. C 42, 438 (1990).
n-D,T Elastic Scattering Plasma is neutron source and target
LLNL-PRES 557971
LLNL-PRES-557971
Next several talks will outline each of the physics models in the codes. What are we missing?
Drive Tr(t), drive spectrum
Implosion dynamics
Bangtime, Vimp, shell thickness, shk timing
Stagnation Physics Yield, PHS, rho-R, Ti
Mix Atwood #
Opacity
EOS
Transport
Kinetics
Nuclear
Au, U
Implosion Performance and NIC Observables Physical models
LLNL-PRES 557971
Details of our electron ion equilibration and stopping power follow in the next 6 vgs
LLNL-PRES-557971
Details for electron ion equilibration model used in NIC calculations
Details for electron ion equilibration
LLNL-PRES 557971
LLNL-PRES-557971
Log Λei is largely from Lee and More
Details for electron ion equilibration
LLNL-PRES 557971
LLNL-PRES-557971
Log( ) for hydrogen: Lee & More (solid), GMS6 (dotted), BPS (dashed)
!ei
Details for electron ion equilibration
9
6
3
0 1022 1023 1024 1025
T=10 KeV
T=1 KeV
T=0.1 KeV
!ei
ne(1/cm3)
LLNL-PRES 557971
LLNL-PRES-557971
Stopping of charged particles is dominated by electron-ion interactions and contains ion-ion scattering
Alpha stopping
dEdx
=CiondEdx i
+CiondEdx e
+CiondEdx b
Contribution from Ions Free e- Bound e-
Ion contribution is small accept at very high Te or electron density
Details for stopping power
LLNL-PRES 557971
LLNL-PRES-557971
Free electron stopping includes degeneracy and full range of ion-e- velocities
Bound electron stopping uses average excitation energy from More UCRL-84991, Sec VII
Alpha stopping
dEdx
=CiondEdx i
+CiondEdx e
+CiondEdx b
Contribution from Ions Free e- Bound e-
Details for stopping power
Stopping of charged particles is dominated by electron-ion interactions and contains ion-ion scattering
LLNL-PRES 557971
LLNL-PRES-557971
For burn conditions dE/dx used in ignition calculations agree with Brown, Preston and Singleton
Te=1 KeV, ne= 5e25
dE/d
x (M
eV/m
icro
n)
.8
.4
0 0 2 4
Vp/Ve Vp/Ve
Te=10 KeV, ne= 1e24
dE/d
x (M
eV/m
icro
n)
0 2 4
.004
.002
0
NIC estimate: solid BPS: Circles Landau & Lifshitz: dashed Li & Petrasso: triangle
LLNL-PRES 557971
End of Intro talk